also, can someone give me tips on how i should study for this class? this class is the 2nd quarter of analysis i'm taking, and we are 4 weeks into the class. so i'd read the book and think i understand the material, only to get stumped on the questions... the midterm exam is on next week friday, so i'm getting really anxious... help!

also, can someone give me tips on how i should study for this class? this class is the 2nd quarter of analysis i'm taking, and we are 4 weeks into the class. so i'd read the book and think i understand the material, only to get stumped on the questions... the midterm exam is on next week friday, so i'm getting really anxious... help!

Actually we can construct ugly functions to satisfy requirements....
For (c) , we can get onto mapping with from [0,1] to [0,1]. Now define f([2,3]) = 1. This will make the function continuous, but the function does not look natural